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Title: On unicity of meromorphic functions due to a result of Yang - Hua (English)
Author: Bai, Xiao-Tian
Author: Han, Qi
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 43
Issue: 2
Year: 2007
Pages: 93-103
Summary lang: English
Category: math
Summary: This paper studies the unicity of meromorphic(resp. entire) functions of the form $f^nf^{\prime }$ and obtains the following main result: Let $f$ and $g$ be two non-constant meromorphic (resp. entire) functions, and let $a\in \mathbb {C}\backslash \lbrace 0\rbrace $ be a non-zero finite value. Then, the condition that $E_{3)}(a,f^nf^{\prime })=E_{3)}(a,g^ng^{\prime })$ implies that either $f=dg$ for some $(n+1)$-th root of unity $d$, or $f=c_1e^{cz}$ and $g=c_2e^{-cz}$ for three non-zero constants $c$, $c_1$ and $c_2$ with $(c_1c_2)^{n+1}c^2=-a^2$ provided that $n\ge 11$ (resp. $n\ge 6$). It improves a result of C. C. Yang and X. H. Hua. Also, some other related problems are discussed. (English)
Keyword: entire functions
Keyword: meromorphic functions
Keyword: value sharing
Keyword: unicity
MSC: 30D35
idZBL: Zbl 1164.30021
idMR: MR2336962
Date available: 2008-06-06T22:50:44Z
Last updated: 2012-05-10
Stable URL:
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